EAS Publications Series, Volume 54, 2012 Oxygen in the Universe G. Stasi ́ nska, N. Prantzos, G. Meynet, S. Sim ́ on-D ́ ıaz, C. Chiappini, M. Dessauges-Zavadsky, C. Charbonnel, H.-G. Ludwig, C. Mendoza, N. Grevesse, M. Arnould, B. Barbuy, Y. Lebreton, A. Decourchelle, V. Hill, P. Ferrando, G. H ́ ebrard, F. Durret, M. Katsuma and C.J. Zeippen November 2011 17 avenue du Hoggar, PA de Courtabœuf, B.P. 112, 91944 Les Ulis cedex A, France First pages of all issues in the series and full-text articles in PDF format are available to registered users at: http://www.eas-journal.org Cover Figure Planetary nebula Abell 39 http://www.noao.edu/image_gallery/html/im0636.html Credit WIYN/NOAO/NSF The spiral galaxy UGC 12158 Credit ESA/Hubble & NASA http://www.spacetelescope.org/images/potw1035a/ Sun http://sdo.gsfc.nasa.gov/data/rules.php Courtesy of NASA/SDO and the AIA, EVE, and HMI science teams. Indexed in: ADS, Current Contents Proceedings – Engineering & Physical Sciences, ISTP r © /ISI Proceedings, ISTP/ISI CDROM Proceedings. ISBN 978-2-7598-0710-9 EDP Sciences Les Ulis ISSN 1633-4760 e-ISSN 1638-1963 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broad-casting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the French Copyright law of March 11, 1957. Violations fall under the prosecution act of the French Copyright Law. c © EAS, EDP Sciences 2012 Printed in UK Authors Affiliations M. Arnould, Institut d’Astronomie et d’Astrophysique, Universit ́ e Libre de Bruxelles, CP. 226, Campus Plaine, Boulevard du Triomphe, 1050 Brussels, Belgium B. Barbuy, Universidade de S ̃ ao Paulo - IAG, Rua do Mat ̃ ao 1226, 05508-900 S ̃ ao Paulo, Brazil C. Charbonnel, Geneva Observatory, University of Geneva, Chemin des Maillettes 51, 1290 Versoix, Switzerland & IRAP, UMR 5572 CNRS, and Universit ́ e de Toulouse, 14 Av. E. Belin, 31400 Toulouse, France C. Chiappini, Leibniz-Institut f ̈ ur Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany A. Decourchelle, Service d’Astrophysique SAp/IRFU/DSM and Laboratoire AIM, CEA-IRFU/CNRS/Universit ́ e Paris Diderot, CEA Saclay, L’Orme des Merisiers, Bˆ at. 709, 91191 Gif-sur-Yvette Cedex, France M. Dessauges-Zavadsky, Geneva Observatory, University of Geneva, Chemin des Maillettes 51, 1290 Versoix, Switzerland F. Durret, UPMC-CNRS, UMR 7095, Institut d’Astrophysique de Paris, 75014 Paris, France P. Ferrando, CEA/DSM/IRFU/ Service d’Astrophysique & UMR APC, CEA Saclay, 91191 Gif-sur-Yvette, France N. Grevesse, Centre Spatial de Li` ege, Universit ́ e de Li` ege, Avenue du Pr ́ e Aily, 4031 Angleur-Li` ege, Belgium and Institut d’Astrophysique et de G ́ eophysique, Universit ́ e de Li` ege, All ́ ee du 6 Aoˆ ut, 17, B5C, 4000 Li` ege, Belgium G. H ́ ebrard, UPMC-CNRS, UMR 7095, Institut d’Astrophysique de Paris, 75014 Paris, France V. Hill, Universit ́ e de Nice Sophia Antipolis, CNRS, Observatoire de la Cˆ ote d’Azur, Bd. de l’Observatoire, BP. 4229, 06304 Nice Cedex 4, France M. Katsuma, Institut d’Astronomie et d’Astrophysique, Universit ́ e Libre de Bruxelles, CP. 226, Campus Plaine, Boulevard du Triomphe, 1050 Brussels, Belgium Y. Lebreton, GEPI & UMR CNRS 8111, Observatoire de Paris, 92195 Meudon Cedex, France and Universit ́ e de Rennes 1, IPR, Bˆ at. 11B, Case 1107, Campus de Beaulieu, 35042 Rennes Cedex, France H.-G. Ludwig, ZAH, Landessternwarte, K ̈ onigstuhl 12, 69117 Heidelberg, Germany C. Mendoza, Centro de F ́ ısica, Instituto Venezolano de Investigaciones Cient ́ ıficas (IVIC), Apdo. Postal 20632, Caracas 1020A, Venezuela, and Centro Nacional de IV C ́ alculo Cient ́ ıfico Universidad de Los Andes (CeCalCULA), Corporaci ́ on Parque Tecnol ́ ogico de M ́ erida, M ́ erida 5101, Venezuela G. Meynet, Geneva Observatory, University of Geneva, Chemin des Maillettes 51, 1290 Versoix, Switzerland N. Prantzos, UPMC-CNRS, UMR 7095, Institut d’Astrophysique de Paris, 75014 Paris, France S. Sim ́ on-D ́ ıaz, Instituto de Astrof ́ ısica de Canarias, 38200 La Laguna, Tenerife, Spain and Departamento de Astrof ́ ısica, Universidad de La Laguna, 38205 La Laguna, Tenerife, Spain G. Stasi ́ nska, LUTH, Observatoire de Paris, CNRS, Universit ́ e Paris Diderot, 5, Place Jules Janssen, 92190 Meudon, France C.J. Zeippen, LERMA, Observatoire de Paris, ENS, UPMC, UCP, CNRS, 5, place Jules Janssen, 92190 Meudon, France List of abbreviations AGB asymptotic giant branch CEL collisional emission line DLA damped lyman alpha system GRB gamma-ray burst IGM intergalactic medium IMF initial mass function ISM interstellar medium LMC Large Magellanic Cloud LTE local thermodynamic equilibrium MS main sequence MW Milky Way NLTE out of local thermodynamic equilibrium ORL optical recombination line QSO quasar RGB red giant branch SFH star formation history SFR star formation rate SMC Small Magellanic Cloud SN supernova SNIa Type Ia supernova SNII Type II supernova SNR supernova remnant SoS solar system WR Wolf-Rayet ZAMS zero-age main sequence NOTATIONS All the wavelenghts are in Angstroms, unless specified otherwise Contents Foreword 1 1 How to Derive Oxygen Abundances 3 1.1 Oxygen abundance scales and notations . . . . . . . . . . . . . . . 3 1.2 Spectroscopic methods . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Basics of line formation . . . . . . . . . . . . . . . . . . . . 5 1.2.1.1 LTE and NLTE . . . . . . . . . . . . . . . . . . . 7 1.2.1.2 Broadening of spectral lines in gaseous media . . . 9 1.2.1.3 Emission lines . . . . . . . . . . . . . . . . . . . . 12 1.2.2 Methods using absorption lines . . . . . . . . . . . . . . . . 14 1.2.2.1 Stellar atmospheres . . . . . . . . . . . . . . . . . 14 Basics of model atmosphere construction. . . . . . 14 Stellar model atmosphere codes. . . . . . . . . . . 17 Oxygen abundance indicators for different stellar types. . . . . . . . . . . . . . . . . . . . . . . . . . 18 Cool stars. . . . . . . . . . . . . . . . . . . . . . . 19 Hydrodynamical model atmospheres of cool stars. 19 Derivation of stellar parameters in cool stars. . . . 22 Effective Temperature . . . . . . . . 23 Gravity . . . . . . . . . . . . . . . . 23 Microturbulence . . . . . . . . . . . . 23 Oxygen abundance indicators in cool stars. . . . . 23 Abundance uncertainties in cool stars. . . . . . . . 26 Hot stars. . . . . . . . . . . . . . . . . . . . . . . . 26 Model atmospheres for hot stars. . . . . . . . . . . 28 Derivation of stellar parameters in hot stars. . . . 29 Abundance analysis in hot stars. . . . . . . . . . . 30 The curve of growth method . . . . . 30 The spectral synthesis method . . . . 31 Abundance uncertainties in hot stars. . . . . . . . 32 1.2.2.2 Interstellar medium . . . . . . . . . . . . . . . . . 34 1.2.3 Methods using emission lines . . . . . . . . . . . . . . . . . 42 1.2.3.1 Photoionised nebulae . . . . . . . . . . . . . . . . 42 1.2.3.2 Collisionally ionised media . . . . . . . . . . . . . 59 viii Oxygen in the Universe 1.3 In situ Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 1.3.1 Meteorites . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 1.3.2 Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . . . 61 1.3.2.1 Cosmic-ray basics . . . . . . . . . . . . . . . . . . 61 1.3.2.2 Measurement techniques . . . . . . . . . . . . . . 62 2 A Panorama of Oxygen in the Universe 65 2.1 The Sun and the solar system . . . . . . . . . . . . . . . . . . . . . 65 2.1.1 Constraints from solar interior modelling and helioseismology . . . . . . . . . . . . . . . . . . . . . . 65 2.1.1.1 Constructing a solar evolution sequence and the present solar interior model . . . . . . . . . . . . . 65 2.1.1.2 Constraining the solar model with the observations 66 2.1.1.3 Results and caveats of solar model calculations . . 71 2.1.1.4 Can we satisfy seismic inferences in solar models based on the new mixture? . . . . . . . . . . . . . 73 2.1.2 The solar atmosphere . . . . . . . . . . . . . . . . . . . . . 75 2.1.2.1 The photosphere . . . . . . . . . . . . . . . . . . . 75 2.1.2.2 The corona . . . . . . . . . . . . . . . . . . . . . . 83 2.1.2.3 Some implications of the new low solar abundance of O and comments . . . . . . . . . . . . . . . . . 84 2.1.2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . 85 2.1.3 Meteorites . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 2.1.3.1 The meteoritic oxygen abundances and isotopic compositions . . . . . . . . . . . . . . . . . . . . . 88 2.1.3.2 Bulk oxygen isotopic compositions of chondrites and achondrites . . . . . . . . . . . . . . . . . . . 89 2.1.3.3 O isotopic anomalies in chondritic components . . 90 2.1.3.4 Oxygen anomalies in stardust grains . . . . . . . . 91 2.1.3.5 Origin of the SoS O isotopic anomalies in chondrite components . . . . . . . . . . . . . . . . . . . . . . 94 2.1.3.6 Origin of the stardust grains with isotopically anomalous oxygen . . . . . . . . . . . . . . . . . . 95 2.2 The Milky Way . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 2.2.1 Solar vicinity . . . . . . . . . . . . . . . . . . . . . . . . . . 98 2.2.1.1 Cosmic rays . . . . . . . . . . . . . . . . . . . . . 98 2.2.1.2 Diffuse interstellar medium . . . . . . . . . . . . . 103 2.2.1.3 H ii regions . . . . . . . . . . . . . . . . . . . . . . 107 2.2.1.4 Early B-type stars . . . . . . . . . . . . . . . . . . 108 2.2.1.5 Solar analogs . . . . . . . . . . . . . . . . . . . . . 110 2.2.1.6 Late type giants . . . . . . . . . . . . . . . . . . . 112 2.2.1.7 Planetary nebulae . . . . . . . . . . . . . . . . . . 113 2.2.1.8 Supernova remnants . . . . . . . . . . . . . . . . . 115 2.2.1.9 Summary . . . . . . . . . . . . . . . . . . . . . . . 116 2.2.2 The Milky Way disk . . . . . . . . . . . . . . . . . . . . . . 119 Contents ix 2.2.2.1 Open clusters . . . . . . . . . . . . . . . . . . . . . 120 2.2.2.2 H ii regions . . . . . . . . . . . . . . . . . . . . . . 120 2.2.2.3 Young stars . . . . . . . . . . . . . . . . . . . . . . 124 2.2.2.4 Cepheids . . . . . . . . . . . . . . . . . . . . . . . 127 2.2.2.5 Planetary nebulae . . . . . . . . . . . . . . . . . . 128 2.2.2.6 Summary of abundance gradients in the Milky Way . . . . . . . . . . . . . . . . . . . . . . . . . . 132 2.2.2.7 Thick disk stars . . . . . . . . . . . . . . . . . . . 133 2.2.3 The Milky Way bulge . . . . . . . . . . . . . . . . . . . . . 137 2.2.3.1 Old stars . . . . . . . . . . . . . . . . . . . . . . . 137 2.2.3.2 Planetary nebulae . . . . . . . . . . . . . . . . . . 140 2.2.3.3 Do planetary nebulae and stars tell the same story? . . . . . . . . . . . . . . . . . . . . . . . . . 143 2.2.4 The Milky Way halo . . . . . . . . . . . . . . . . . . . . . . 143 2.2.4.1 Field stars . . . . . . . . . . . . . . . . . . . . . . 143 2.2.4.2 Planetary nebulae . . . . . . . . . . . . . . . . . . 145 2.2.4.3 Globular clusters . . . . . . . . . . . . . . . . . . . 147 2.3 The local Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 2.3.1 The Magellanic Clouds . . . . . . . . . . . . . . . . . . . . . 150 2.3.2 Abundance gradients in spiral galaxies . . . . . . . . . . . . 155 2.3.2.1 M 33 . . . . . . . . . . . . . . . . . . . . . . . . . . 157 2.3.2.2 M 101 . . . . . . . . . . . . . . . . . . . . . . . . . 160 2.3.2.3 M 31 . . . . . . . . . . . . . . . . . . . . . . . . . . 160 2.3.2.4 NGC 300 . . . . . . . . . . . . . . . . . . . . . . . 162 2.3.3 Galaxies that stopped forming stars . . . . . . . . . . . . . 164 2.3.4 The mass-metallicity relation of galaxies . . . . . . . . . . . 166 2.3.5 The hot gas in clusters of galaxies . . . . . . . . . . . . . . 170 2.4 The high-redshift Universe . . . . . . . . . . . . . . . . . . . . . . . 175 2.4.1 Oxygen abundance in galaxies up to z 1 . . . . . . . . . 175 2.4.2 Oxygen abundances in galaxies beyond z 1 . . . . . . . . 177 2.4.3 Oxygen abundances in QSO absorption line systems and GRB hosts . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 2.4.4 Mass-metallicity relation in QSO absorption line systems 185 3 Oxygen Production and Destruction 187 3.1 Oxygen and nuclear physics . . . . . . . . . . . . . . . . . . . . . . 187 3.1.1 Some generalities about thermonuclear reaction rates in astrophysics conditions . . . . . . . . . . . . . . . . . . . 187 3.1.2 Main reactions . . . . . . . . . . . . . . . . . . . . . . . . . 188 3.1.2.1 15 N ( p , γ ) 16 O . . . . . . . . . . . . . . . . . . . . 188 3.1.2.2 17 O ( p , α ) 14 N and 17 O ( p , γ ) 18 F . . . . . . . . . . 189 3.1.2.3 18 O ( p , α ) 15 N . . . . . . . . . . . . . . . . . . . . 191 3.1.2.4 12 C ( α , γ ) 16 O . . . . . . . . . . . . . . . . . . . . 194 3.1.2.5 13 C ( α , n ) 16 O . . . . . . . . . . . . . . . . . . . . 199 3.1.2.6 14 N ( α , γ ) 18 F . . . . . . . . . . . . . . . . . . . . . 201 x Oxygen in the Universe 3.1.2.7 18 O ( α , γ ) 22 Ne . . . . . . . . . . . . . . . . . . . . 202 3.1.3 Other charged-particle reactions involving the stable oxygen isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 3.1.4 A brief analysis of the impact of nuclear uncertainties on the stellar oxygen yields . . . . . . . . . . . . . . . . . . . . . . 204 3.1.5 Neutron captures involving the oxygen isotopes . . . . . . . 206 3.1.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 3.2 Stellar nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . 207 3.2.1 Stellar evolution in a nutshell . . . . . . . . . . . . . . . . . 207 3.2.1.1 The main energy reservoirs . . . . . . . . . . . . . 208 3.2.1.2 Perfect gas and degenerate gas . . . . . . . . . . 208 3.2.1.3 Evolution under non-degenerate and degenerate conditions . . . . . . . . . . . . . . . . . . . . . . . 211 3.2.1.4 The five mass ranges . . . . . . . . . . . . . . . . 211 3.2.2 Massive stars . . . . . . . . . . . . . . . . . . . . . . . . . . 213 3.2.2.1 A reference case: a 25 M star . . . . . . . . . . . 213 3.2.2.2 Effects of mass, metallicity, rotation, etc. . . . . . 221 3.2.2.3 Yields . . . . . . . . . . . . . . . . . . . . . . . . 230 3.2.2.4 Observational probes . . . . . . . . . . . . . . . . 230 3.2.2.5 Core-collapse supernovae . . . . . . . . . . . . . . 233 3.2.2.6 Pair-instability supernovae . . . . . . . . . . . . . 234 3.2.3 Low- and intermediate-mass stars . . . . . . . . . . . . . . . 235 3.2.3.1 A reference case: a 5 M star . . . . . . . . . . . 235 3.2.3.2 Effects of mass, metallicity, rotation, etc... . . . . 241 3.2.3.3 Stellar yields . . . . . . . . . . . . . . . . . . . . . 248 3.2.3.4 Observational probes . . . . . . . . . . . . . . . . 248 3.2.4 Binary stars . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 3.3 Final comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 4 The Evolution of Oxygen in Galaxies 255 4.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 4.2 Chemical evolution modelling . . . . . . . . . . . . . . . . . . . . . 256 4.2.1 Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 4.2.2 Stellar properties: lifetimes, residues and yields . . . . . . . 259 4.2.3 Initial Mass Function . . . . . . . . . . . . . . . . . . . . . 264 4.2.4 Star Formation Rate . . . . . . . . . . . . . . . . . . . . . . 266 4.2.5 Gaseous flows and stellar feedback . . . . . . . . . . . . . . 269 4.2.6 Analytical solutions: the instantaneous recycling approximation . . . . . . . . . . . . . . . . . . . . . . . . . 270 4.3 Chemical evolution of the Milky Way . . . . . . . . . . . . . . . . . 273 4.3.1 The solar vicinity . . . . . . . . . . . . . . . . . . . . . . . . 273 4.3.1.1 Observables . . . . . . . . . . . . . . . . . . . . . . 275 4.3.1.2 The local metallicity distribution of long-lived stars . . . . . . . . . . . . . . . . . . . . . . . . . . 276 4.3.1.3 The local age-metallicity relationship . . . . . . . 280 Contents xi 4.3.1.4 A brief history of the solar neighbourhood . . . . 280 4.3.1.5 The local evolution of D/O . . . . . . . . . . . . . 282 4.3.2 The Galactic halo . . . . . . . . . . . . . . . . . . . . . . . 283 4.3.3 The Galactic bulge . . . . . . . . . . . . . . . . . . . . . . . 286 4.3.4 The Galactic disk . . . . . . . . . . . . . . . . . . . . . . . . 287 4.3.4.1 Radial profiles as witnesses of the disk formation history . . . . . . . . . . . . . . . . . . . . . . . . 288 4.3.4.2 The thin disk abundance gradient: interpretation with purely chemical evolution models . . . . . . . 289 4.3.4.3 Is the IMF variable? Clues from the oxygen abundance gradient . . . . . . . . . . . . . . . . . 296 4.3.4.4 The evolution of the oxygen gradient . . . . . . . 298 4.3.5 The special case of globular clusters: direct pollution . . . . 299 4.4 The other spiral galaxies . . . . . . . . . . . . . . . . . . . . . . . . 301 4.4.1 M 31: a Milky Way twin? . . . . . . . . . . . . . . . . . . 302 4.4.2 M 33 and M 101: two very different spirals with very different gradients . . . . . . . . . . . . . . . . . . . . . . . 304 4.4.3 NGC 300: an almost bulge-less spiral galaxy . . . . . . . . 307 4.4.4 A general picture for the formation of disk galaxies . . . . . 309 4.5 Oxygen in the largest MW satellites: the Magellanic Clouds . . . . 310 4.6 The mass-metallicity relation of galaxies . . . . . . . . . . . . . . . 313 4.7 The global oxygen budget in the Universe . . . . . . . . . . . . . . 316 A The Atomic Physics of Oxygen 319 A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 A.2 Collisionally excited lines . . . . . . . . . . . . . . . . . . . . . . . 320 A.2.1 O i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 A.2.2 O ii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 A.2.3 O iii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 A.2.4 O iv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 A.2.5 O v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 A.2.6 O vi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 A.2.7 O vii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 A.2.8 O viii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 A.3 Optical recombination lines . . . . . . . . . . . . . . . . . . . . . . 330 A.4 Charge transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 A.5 K-shell photoabsorption . . . . . . . . . . . . . . . . . . . . . . . . 332 A.6 Opacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 References 337 Oxygen in the Universe G. Stasi ́ nska et al. EAS Publications Series, 54 (2012) 1 Foreword This book is the result of a collaboration between specialists of various areas of astronomy to summarise what we understand of the production and distribution of oxygen in the Universe. A large part is devoted to the methods of oxygen abundance determination in various media, as those are the fundaments on which our knowledge is built. Why concentrate on oxygen? Oxygen is the most abundant of the metals, its abundance can be measured in many sites and with a variety of techniques, its formation process is now rather well understood: yet there are many unsolved questions. We believe that it is by showing the problems and facing them that progress is better made. Following the thread of oxygen, the reader can gain a view of the Universe which is quite different from the perspective usually adopted in manuals, and therefore hopefully rewarding. We believe that this book is suitable for students, provided that they have sufficient background knowledge in astrophysics. This volume contains a lot of original material in the form of figures and tables as well as an extensive list of references. However, since this book took about 4 years to get assembled, and its parts were written at different epochs, not all the references have been updated. The field is progressing so fast that any update would have quickly become obsolete anyway. As a matter of fact, the major aim of this book is not to describe the latest results, but rather to provide the reader with tools for a deeper understanding of how these results are obtained. This is why this book not only provides a careful mapping of oxygen in the Universe but also introduces some fundamental astronomical concepts ( e.g. theory of line formation, stellar evolution principles, basic equations for chemical evolution of galaxies), and discusses the methods to derive the chemical composition of astronomical bodies (stars, nebulae, cosmic rays, meteorites, etc.) and their uncertainties. The reliability of the atomic and nuclear data is also addressed. We undertook this collective endeavour so that the reader could benefit from the best of our experience in our respective fields, perhaps at the expense of ho- mogeneity in style or notation. We hope that the usefulness of this book will overcome its imperfections. We warmly thank the Laboratory Universe and Theories of the Paris Observatory for the financial support which made this project feasible. The authors c © EAS, EDP Sciences 2012 DOI: 10.1051/eas/1254000 Oxygen in the Universe G. Stasi ́ nska et al. EAS Publications Series, 54 (2012) 3–63 Chapter 1 HOW TO DERIVE OXYGEN ABUNDANCES 1.1 Oxygen abundance scales and notations Before describing the many ways to determine the abundance of oxygen in various regions of the Universe, let us first present the different scales and notations that are used for this purpose. For historical reasons, each field of astronomy has developed its own metrics. In astronomy, the word abundance applied to an element, for example oxygen, usually refers to the ratio of its number density, n (O), to that of hydrogen, n (H). It is usually simply written O/H. The abundance of the element is often given on a logarithmic scale in which the value for hydrogen is 12: A (O) = log (O) = log n (O) /n (H) + 12 (1.1) This is the so-called astronomical scale Another important quantity is the mass fraction of an element. For oxygen, it is written X (O) and given by X (O) = μ O n (O) /n (H) ∑ μ E n (E) /n (H) , (1.2) where μ E is the atomic weight of element E and the summation in the denominator includes all the elements. The value of the denominator is the same in all the parts of the Universe and does not change with time. The metallicity, Z , is the sum of the mass fractions of all the elements heavier than helium 1 . Due to its high cosmic abundance, oxygen accounts for almost half of the total mass fraction of metals in the Sun. In studies dealing with atmospheres of cool stars, the abundances of the ele- ments are traditionally expressed in logarithm with respect to the solar value and use a notation with brackets. For oxygen it may be expressed [O / H] = log(O / H) − log(O / H) (1.3) 1 In astronomy, all the elements except H and He are called heavy elements or metals , although not all of them are heavy elements or metals in the chemical sense. c © EAS, EDP Sciences 2012 DOI: 10.1051/eas/1254001 4 Oxygen in the Universe This has the advantage of an easy visualisation of how much the chemical compo- sition of a given region differs from that in the Sun. The drawback is that when- ever the solar chemical composition is revised – and this happened several times recently – a simultaneous revision of all the previously published abundances is required as well, if those are to be compared with the abundances in other celestial bodies. For this reason, it would seem much more logical to express abundances with respect to hydrogen. However, the reason for using such a scale in cool star atmospheres is that abundances are determined with respect to a reference value – usually the solar one – and not in absolute value. For objects in which hydrogen is only a trace element, like in the atmospheres of some evolved stars, a scale based on hydrogen would not be appropriate and one rather uses mass fractions. The meteoritic scale (also called cosmochemical scale ) uses numbers of atoms relative to 10 6 atoms of Si. In ionised nebulae, the metallicity is generally expressed in units of solar metal- licity denoted by Z . Thus, a nebula with twice the solar metallicity would have Z = 2 Z . Since oxygen represents a large fraction of the total mass of the metals, and since the abundances of most elements contributing significantly to the metal- licity generally vary in lockstep in the Universe, the oxygen abundance in such a nebula would be almost equal to twice the solar value – except if the nebula is close to a region of production of oxygen or of other elements contributing significantly to the metallicity. Therefore, in practice, the metallicity Z has a slightly different meaning for the stellar and the nebular astrophysicists. In both cases, oxygen plays a dominant role in the definition. In nebular astronomy, as just mentioned, the metallicity is synonym of the oxygen abundance. This is justified by the fact that oxygen generally plays a dominant role in the cooling. In stellar astronomy, it is strongly related to the oxygen abundance, since oxygen is the element that contributes most to the total mass of elements heavier than metals. However, the dominant sources of opacity that control the stellar internal structure as well as stellar evolution are iron and other heavy elements. In first approximation, the oxygen and iron contents in astronomical objects vary in lockstep, so the distinction between the two definitions does not lead to major problems. However, it is now known that the O/Fe ratio is not exactly constant in the Universe, but is a function of the history of star formation (see Chapter 4). Besides, the abundance of oxygen (and metals) that is considered as the solar value has changed several times (see Chapter 2). Therefore, the word metallicity must be correctly deciphered in every paper. Absorption line studies often give the chemical composition in number of atoms per 10 6 H atoms (the unit is abbreviated as ppm, for part per million ). One thus has to adapt to different scales and units according to the objects un- der consideration, and be able to easily transform one into another when changing the area of interest. As an illustration, we give in the table below the value of the solar oxygen abundance in different scales for two different estimates that have been widely Chapter 1: How to Derive Oxygen Abundances 5 Table 1.1. The solar oxygen abundance in various scales. Reference O/H A (O) Z (O) [O/H] a AG89 [O/H] b Aspl09 AG89 a 8 51 × 10 − 4 8.93 9 60 × 10 − 3 0 0.24 Aspl09 b 4 90 × 10 − 4 8.69 5 77 × 10 − 3 − 0 24 0 a Anders & Grevesse (1989) b Asplund et al. (2009) quoted in the literature as a reference: Anders & Grevesse (1989) and Asplund et al. (2009). 1.2 Spectroscopic methods 1.2.1 Basics of line formation The emission of light by an astronomical object is the result of interactions be- tween its constituting matter and the ambient electromagnetic field. The discrete character of possible internal energy states of the involved matter particles (here atoms or molecules) often gives such interactions the character of resonances taking place at specific (temporal) frequencies. The frequency spectrum exhibits localised intensity features – spectral lines . If the intensity in a spectral line is larger than in its immediate spectral vicinity one speaks of an emission line , in the case of a reduced intensity, of an absorption line The lines are often superimposed on a slowly changing background – the spectral continuum . A spectral line encodes properties of the particles responsible for its formation and the environment in which the formation took place. In particular, spectral lines allow the derivation of the abundance of the interacting particles and thus the study of the chemical composition of astronomical objects by remote sensing – in astronomy obviously a very valuable capability. Depending on environment the abundance of oxygen is derived from emission or absorption lines whose specific aspects and intricacies of formation are discussed in the corresponding sections below. For now, we leave out the complexities of the microscopic processes governing the emission and absorp- tion of light and give an elementary, phenomenological account of the formation of spectral lines to provide the reader with an intuitive picture 2 A beam of light travelling through a medium in the positive direction s expe- riences a change of intensity according to dI ν ds = − ρχ ν ( I ν − S ν ) , (1.4) 2 We would like to acknowledge inspiration for the following considerations obtained from R.J. Rutten’s lecture notes on “Radiative Transfer in Stellar Atmospheres”. We further assume that the reader is familiar with the basic definition and meaning of intensity, source function and absorption coefficient. 6 Oxygen in the Universe where I ν is the specific intensity per frequency interval, χ ν the frequency-dependent mass absorption coefficient, S ν the source function per frequency interval and ρ the mass density. Introducing the optical depth τ ν ( s ) ≡ ∫ s 0 ρχ ν ds ∗ (1.5) measured from the origin to coordinate s in the direction of beam propagation we can write Equation (1.4) as dI ν dτ ν = − I ν + S ν (1.6) The general solution of the differential Equation (1.6) in the interval [0 , τ ν ] can be written as I ν ( τ ν ) = I ν (0) e − τ ν + ∫ τ ν 0 S ν ( t ν ) e − ( τ ν − t ν ) dt ν (1.7) with I ν (0) ≡ I ν ( τ ν = 0). This is an example of the so-called formal solution of a given radiative transfer problem, i.e. the solution of the radiative transfer equation for a given source function as function of optical depth. While generally the mass density and the absorption coefficient are complex functions of location s we now consider a very simple model: a homogeneous medium of finite geometrical thickness – say, a gas cloud – stretching from s = 0 to s = d in which source function, mass density and absorption coefficient are constant. Moreover, we assume it is illuminated at s = 0 with radiation of intensity I ν (0), and an observer records the emitted intensity at s = d . We note in passing that if the observer were located at s > d and no matter were present in-between s = d and the observer, the recorded intensity would remain the same: the specific intensity is a distance-independent quantity. For a homogeneous medium the integral in Equation (1.7) can be easily solved analytically, and one obtains I ν ( d ) = S ν + ( I ν (0) − S ν ) e − τ ν ( d ) (1.8) We now evaluate Equation (1.8) at frequencies within and outside of a line. The presence of a line adds some extra absorption and increases the optical depth at s = d from the continuum optical depth τ c to τ l+c = τ l + τ c . For the difference of the intensity in the line including the contributions from the continuum I l+c ν and the neighbouring continuum I c ν we obtain from Equation (1.8) I l+c ν − I c ν = [ S ν − I ν (0)] e − τ c ( 1 − e − τ l ) (1.9) From Equation (1.8) a first conclusion can be drawn for our simple model. In case of a very large optical thickness in the continuum τ c ( d ) 1 and consequently even more so in the line, the observed intensity corresponds to the source function in the cloud S ν In the case of local thermodynamic equilibrium (LTE) the source function within a spectral line and the continuum are identical and equal to the Chapter 1: How to Derive Oxygen Abundances 7 black body radiation function 3 B ν . In other words, an isothermal, optically thick medium in LTE emits a line-free continuum given by the black body radiation function of the given temperature. For the formation of a spectral line at least one of the conditions of thermal homogeneity, large optical thickness or LTE has to be violated. However, in astronomical objects all three conditions are hardly ever met simultaneously so that the formation of spectral lines is a ubiquitous phenomenon. From Equation (1.9) we see that depending on the optical thickness in the continuum and the intensity of the illuminating radiation I ν (0) the “modulation” of the optical depth scale by the presence of the line is responsible for the formation of a spectral line. In case that the background illumination is weak I ν (0) < S ν the line appears in emission. If the background illumination is increased I ν (0) > S ν the line appears in absorption. At first sight it may appear counter-intuitive that by adding intensity a previously brighter spectral feature becomes dark. The reason is that the added background intensity is more strongly blocked in the line than in the continuum and cannot contribute anymore to the observed line intensity. One might take this situation as a crude model of a stellar atmosphere while the lack of background illumination is a typical situation in nebulae. From the discussion it is clear that emission and absorption lines are of the same nature, and that broadening mechanisms operate in the same way. Their distinction in the following sections is motivated by differences in their practical analysis in the various astronomical environments. 1.2.1.1 LTE and NLTE For calculating the detailed interaction between matter and radiation one needs to know the population numbers of the involved quantum states – of the ra- diating atoms or molecules as well as of the radiation field itself. For render- ing this complex problem tractable the approximation of Local Thermodynamic Equilibrium (LTE) was introduced. Depending on the physical system the LTE approximation can be refined by explicitly considering non-equilibrium processes which is referred to as the treatment of the problem in Non Local Thermodynamic Equilibrium (NLTE, or non-LTE). In the following we give a brief discussion of the concepts in connection to the formation of spectral lines. The second law of thermodynamics states that a closed thermodynamic sys- tem (a system with a large number of internal degrees of freedom) always evolves towards a state of larger disorder – into thermodynamic equilibrium. Under such circumstances the system can be characterised by a single temperature, and the populations of the various quantum states – in NLTE parlance usually referred to as level populations – can be calculated without explicit knowledge of the micro- scopic processes populating and de-populating a particular state. Obviously, this 3 Often also called the Kirchhoff-Planck function. 8 Oxygen in the Universe is a tremendous simplification of the situation since the level populations can be calculated from statistics known from equilibrium thermodynamics: • the levels within an atom or molecule are populated according to Boltzmann statistics • the ionisation of atoms is following Saha-Boltzmann statistics • analogous to ionisation processes the association and dissociation of molecules follows the mass action (or Guldberg-Waage) law • the thermal motion of the matter particles follows Maxwell statistics • the source function is given by the black body function. While indeed the above conditions alleviate the solution of the overall problem tremendously, one has to keep in mind that depending on the number of involved plasma constituents theoretical calculations can still be rather cumbersome even when assuming strict LTE. They can involve the solution of large systems of equations. Moreover, the partition functions of all involved species need to be known, hence demanding detailed knowledge of all relevant energy levels of the constituents − information which is not always available. Stellar atmospheres as well as interstellar gas clouds (astrophysical systems which will be of particular interest in later sections) are open systems since, e.g. energy is flowing through them driven by temperature gradients. Hence, the con- ditions of thermodynamic equilibrium cannot be met globally. However, equilibria may in fact be established locally (motivating the term local thermodynamic equi- librium) in regions over which the physical conditions vary little. Since such local sub-systems interact with their environment two conditions need to be fulfilled such that local thermodynamic equilibrium can indeed be reached: (i) there is sufficient time that microscopic randomising processes can take effect to establish equilibrium and (ii) there is no external forcing inhibiting processes necessary for establishing equilibrium. In astrophysical plasmas collisions among the particles due to their thermal motion are often the main driving agent towards thermodynamic equilibrium. Electrons are particularly effective since they have a large interaction cross section (due to their charge) and high thermal velocity (due to their small mass). Ther- modynamic equilibrium conditions are thus usually established on a time scale controlled by the time interval between particle collisions. In the optically thin case the radiation field has a non-local character, inter-connecting regions where different physical conditions – particularly temperatures – prevail. This tends to drive the coupled systems out of LTE. A typical situation is encountered in stellar atmospheres where the hot radiation field emerging at deeper layers is impinging on higher atmospheric layers of lower temperature. While collisions try to estab- lish level populations corresponding to the local kinetic temperature of the gas the radiation field introduces changes of the level populations corresponding to a higher temperature. The competition between the various processes determines